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This paper describes the use of non-linear formant trajectories to model speech dynamics. The performance of the non-linear formant dynamics model is evaluated using HMM-based speech synthesis experiments, in which the 12 dimensional parallel formant synthesiser control parameters and their time derivatives are used as the feature vectors in the HMM. Two types of formant synthesiser control parameters, named piecewise constant and smooth trajectory parameters, are used to drive the classic parallel formant synthesiser. The quality of the synthetic speech is assessed using three kinds of subjective tests. This paper shows that the non-linear formant dynamics model can improve the performance of HMM-based speech synthesis.